Question: 7 people can paint 3 walls in 31 minutes. How many minutes will it take for 8 people to paint 7 walls? Round to the nearest minute.
Explanation: We know the following about the number of walls $w$ painted by $p$ people in $t$ minutes at a constant rate $r$ $w = r \cdot t \cdot p$ $\begin{align*}w &= 3\text{ walls}\\ p &= 7\text{ people}\\ t &= 31\text{ minutes}\end{align*}$ Substituting known values and solving for $r$ $r = \dfrac{w}{t \cdot p}= \dfrac{3}{31 \cdot 7} = \dfrac{3}{217}\text{ walls painted per minute per person}$ We can now calculate the amount of time to paint 7 walls with 8 people. $t = \dfrac{w}{r \cdot p} = \dfrac{7}{\dfrac{3}{217} \cdot 8} = \dfrac{7}{\dfrac{24}{217}} = \dfrac{1519}{24}\text{ minutes}$ $= 63 \dfrac{7}{24}\text{ minutes}$ Round to the nearest minute: $t = 63\text{ minutes}$